20 CHEMICAL ENGINEERING Size of Compound Engines.—For two cylinders developing the same power, the receiver pressure Po (pounds per square inch, absolute) is given by loge PO = K(log« R-----JT — 1) — loge(R -T- P), R being the maximum volume of steam in the low-pressure cylinder divided by volume of steam at cut-off in high-pressure cylinder. If At, Ah are the corresponding effective piston areas and C = RP0 -*-P = Ai -f- Ah, the mean effective pressures are Pml = (P -i- JB) (1 + loge C) - p Pmh = Pml X C and the horsepower of the whole engine is fpmiLNAi 16,500 Discussion of Factors.—The value of C is usually from 3 to 4 in non-condensing and from 4 to 5 in condensing engines. It should vary directly with R. If it is made too great, the engine will, though probably economical of steam, be costly to build and deficient in overload capacity; for the maximum power of the engine, working as a compound, is obtained when R = C3 the low-pressure cylinder receiving steam at full boiler pressure, and the high-pressure doing no work. In usual practice, the low-pressure cylinder is not built to withstand full boiler pressure, but only a lower pressure Pi, which is realized either by raising the receiver pressure to PI or (in unusual emergencies) by running the two cylinders as two simple engines between the pressure limits P and p and PI and p, respectively. P will range from 115 to 265, preferably not under 165 for condensing engines. Values of p, non-condensing, are from 15 to 17; condensing, 1 or 2, but preferably 1. Half the tabulated values of R may be used for compound non-condensing engines. The use of jackets warrants high values for R. High values are indicated when fuel is costly or the load is steady. Values of / may be taken as those given for simple engines with the \/R ratio of expansion. Brake Horsepower.—The power lost in friction, f.hp., may be regarded as constant so that the brake horsepower, b.hp., is i.hp. — f.hp. at all loads. The mechanical efficiency at full load is M = b.hp./i.hp. = (i.hp. — f.hp.)/i.hp. i.hp. being taken at full load. As the load increases, the mechanical efficiency steadily increases. At the Q proportion of full rated load, it is M, = (Q -f M - 1)/Q In a double-acting single-cylinder engine F = pmASM/Si where F = tractive or hauling force exerted, in pounds, pm = average net piston pressure (the mean effective pressure, in expansive engines), pounds per square inch, A = piston area, square inches, S = piston speed, feet per minute, M = mechanical efficiency, and Si = speed of part at which the tractive force is applied—the peripheral speed of locomotive drivers or of hoisting engine drum—feet per minute. Steam-engine Economy.—The steam rate of an engine depends primarily on the initial pressure and superheat, back pressure and ratio of expansion. The following tables refer to perfect engines (Rankine cycle). The probable